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Have any aircraft ever been attacked by chemical, biological, radiological or nuclear weapons? Information security compromises?
Have any aircraft, military or civilian, ever been attacked by chemical, biological, radiological or nuclear weapons?
Terrorist attacks and test firings included. Attacks on persons on-board the aircraft (rather than the aircraft itself) included.
Information security attacks on the aircraft itself (such as computer viruses) would also be of interest, although I'll exclude jamming of communications and sensors such as radar.
Sources I've already consulted:

Airport and Aviation Security, Elias
USACBRN School, Wikipedia
The Jihadist CBRN Threat, Stratfor
Flying High, Flying Safe, Wolff
Practical Aviation Security, Price & Forrest
Counterterrorism: A Reference Handbook, Steven & Gunaratna

Definition of 'chemical weapon': sure, explosives are made out of chemicals (as is everything else) but I'm talking about chemical weapons as defined by the Organisation for the Prohibition of Chemical Weapons:

The term chemical weapon is applied to any toxic chemical or its precursor that can cause death, injury, temporary incapacitation or sensory irritation through its chemical action. Munitions or other delivery devices designed to deliver chemical weapons, whether filled or unfilled, are also considered weapons themselves.
The toxic chemicals that have been used as chemical weapons, or have been developed for use as chemical weapons, can be categorised as choking, blister, blood, or nerve agents. The most well known agents are as follows: choking agents—chlorine and phosgene, blister agents (or vesicants)—mustard and lewisite, blood agents—hydrogen cyanide, nerve agents—sarin, soman, VX.

For 'radiological weapons', I'm not talking about visible electromagnetic radiation (light) or invisible electromagnetic radiation (radio etc) but rather radiological dispersion devices, defined by the US Department of Defence as:

any device, including any
weapon or equipment, other than a nuclear explosive device, specifically designed to employ
radioactive material by disseminating it to cause destruction, damage, or injury by means of the
radiation produced by the decay of such material

Ford, J. (March 1998). Radiological Dispersion Devices: Assessing the transnational threat. National Defense University - Institute for National Strategic Studies - Strategic Forum, No. 136. as cited in Rickert, Paul R., "The Likely Effect of a Radiological Dispersion Device" (2005). Faculty Publications and Presentations. Paper 47.
'Biological weapons' as defined by the United Nations:

Biological weapons are complex systems that disseminate disease-causing organisms or toxins to harm or kill humans, animals or plants. They generally consist of two parts – a weaponized agent and a delivery mechanism. In addition to strategic or tactical military applications, biological weapons can be used for political assassinations, the infection of livestock or agricultural produce to cause food shortages and economic loss, the creation of environmental catastrophes, and the introduction of widespread illness, fear and mistrust among the public.
Almost any disease-causing organism (such as bacteria, viruses, fungi, prions or rickettsiae) or toxin (poisons derived from animals, plants or microorganisms, or similar substances produced synthetically) can be used in biological weapons. The agents can be enhanced from their natural state to make them more suitable for mass production, storage, and dissemination as weapons. Historical biological weapons programs have included efforts to produce: aflatoxin; anthrax; botulinum toxin; foot-and-mouth disease; glanders; plague; Q fever; rice blast; ricin; Rocky Mountain spotted fever; smallpox; and tularaemia, among others.

a conventional rocket is much more effective and cheaper (happened at least 3 times of the top of my head)

@ratchetfreak: Yes, many aircraft have been attacked with conventional rockets, missiles and bombs. But my question is about CBRN and informational attacks.

and a conventional rocket uses chemical explosives, so it's technically a chemical weapon ;) Many also use radiation of some sort (IR, radar, etc.) to home in on their target...

@jwenting: I've added definitions.

What immediately comes to mind is the Lockheed XF-90, an early US jet fighter, which had a very strong and heavy airframe. For that reason, the second prototype (of only two ever built) was subjected in 1952 to three nuclear bomb tests in the Nevada desert (not in flight, however. It was sitting on the ground).
At this time, an unguided nuclear-armed air-to-air missile, the Douglas AIR-2 Genie, was developed and tested once in 1957. Several USAF officers were standing below the test spot, but no aircraft were used as targets. The missile was fired by an F-89 Scorpion and could be carried by the F-101, the F-104 and the F-106.
The purpose of the AIR-2 was to attack tight formations of Tupolev Tu-4 bombers in the days before guided SAM missiles were available.
I am sure the Russians had their own score of nuclear tests on aircraft, but I do not know anything specific.

but what is the point of it?
A plane is too small of a target, a SAM missile is more than enough to shoot down a jet.

@TaherElhouderi simple. Shoot a 1kt nuke in the general direction of a formation of bombers, explode it in the middle of the formation, and you kill all of them. No need for complex guidance systems (which were in their infancy at the time, large, cumbersome, unreliable, and heavy).

I've found a few instances myself:
Radiological
As part of the Litvinenko case:

During the investigation into his death it was learned that a number of British Airways aircraft that flew between Moscow and London had been contaminated with the radioactive material [Polonium-210].
... 33,000 passengers potentially exposed ... very low traces ... the risk to public health proved to be low

Source is Aviation Security International, April 2013
Information Security

In theory, a hacker could use a plane's onboard WiFi signal or inflight entertainment system to hack into its avionics equipment, potentially disrupting or modifying satellite communications, which could interfere with the aircraft's navigation and safety systems, Santamarta said.
He acknowledged that his hacks have only been tested in controlled environments, such as IOActive's Madrid laboratory, and they might be difficult to replicate in the real world. Santamarta said he decided to go public to encourage manufacturers to fix what he saw as risky security flaws.
Representatives for Cobham, Harris, Hughes and Iridium said they had reviewed Santamarta's research and confirmed some of his findings, but downplayed the risks.

Hacker says to show passenger jets at risk of cyber attack, Reuters

it's possible to take control of aircraft flight systems and communications using an Android smartphone and some specialized attack code.
Hugo Teso, a security researcher at N.Runs and a commercial airline pilot, spent three years developing the code, buying second-hand commercial flight system software and hardware online and finding vulnerabilities within it. His presentation will cause a few sleepless nights among those with an interest in aircraft security.
Teso's attack code, dubbed SIMON, along with an Android app called PlaneSploit, can take full control of flight systems and the pilot's displays. The hacked aircraft could even be controlled using a smartphone's accelerometer to vary its course and speed by moving the handset about.
"You can use this system to modify approximately everything related to the navigation of the plane," Teso told Forbes. "That includes a lot of nasty things."

Researcher hacks aircraft controls with Android smartphone, The Register
See also: Conference presentation from security researcher Hugo Teso
However, the FAA issued a response in a statement to journalists:

The FAA is aware that a German information technology consultant has alleged he has detected a security issue with the Honeywell NZ-2000 Flight Management System (FMS) using only a desktop computer.
The FAA has determined that the hacking technique described during a recent computer security conference does not pose a flight safety concern because it does not work on certified flight hardware.
The described technique cannot engage or control the aircraft’s autopilot system using the FMS or prevent a pilot from overriding the autopilot. Therefore, a hacker cannot obtain “full control of an aircraft” as the technology consultant has claimed.

as did the EASA:

For more than 30 years now, the development of certifiable embedded software has been following strict guidance and best practices that include in particular robustness that is not present on ground-based simulation software.

and equipment manufacturer Rockwell Collins:

Today’s certified avionics systems are designed and built with high levels of redundancy and security.
The research by Hugo Teso involves testing with virtual aircraft in a lab environment, which is not analogous to certified aircraft and systems operating in regulated airspace.

FAA and security researchers at odds over airplane hack security, Sophos Naked Security, 16 April 2013
Information Security (?) - drone
Iran claims to have caused a US drone to land through a cyber-attack, in Dec 2011.

ISTANBUL, TURKEY — Iran guided the CIA's "lost" stealth drone to an intact landing inside hostile territory by exploiting a navigational weakness long-known to the US military, according to an Iranian engineer now working on the captured drone's systems inside Iran.
Iranian electronic warfare specialists were able to cut off communications links of the American bat-wing RQ-170 Sentinel, says the engineer, who works for one of many Iranian military and civilian teams currently trying to unravel the drone’s stealth and intelligence secrets, and who could not be named for his safety.
Using knowledge gleaned from previous downed American drones and a technique proudly claimed by Iranian commanders in September, the Iranian specialists then reconfigured the drone's GPS coordinates to make it land in Iran at what the drone thought was its actual home base in Afghanistan.

http://www.csmonitor.com/World/Middle-East/2011/1215/Exclusive-Iran-hijacked-US-drone-says-Iranian-engineer-Video
US confirms the drone was downed but does not confirm a successful cyberwarfare attack.
http://en.wikipedia.org/wiki/Iran%E2%80%93U.S._RQ-170_incident

I'm pretty sure that in-flight WiFi systems and IFE systems are not connected to flight control or other avionics systems in any way that could possibly allow the avionics to receive commands from them. I don't think such a design would ever be certificated.

@eirab, you're certainly right that they shouldn't be. But by their nature infosec exploits are unintended and unforeseen. In this presentation, security researcher Hugo Teso lays out what he claims is a working exploit. If you're a pilot then I'm sure details of the various aircraft systems involved will be clearer to you than to me. I believe example code has been passed to the EASA (etc) but not publicly released (for obvious reasons).

The FAA dismissed those claims. The FAA has determined that the hacking technique described during a recent computer security conference does not pose a flight safety concern because it does not work on certified flight hardware. The described technique cannot engage or control the aircraft’s autopilot system using the FMS or prevent a pilot from overriding the autopilot. While I don't fly airliners (I do fly small aircraft,) I have been involved in aviation from the engineering side. From my experience on that side, I doubt the FAA would ever certify a design that provided remote vectors.

See the Update section of this article for the full quote from the FAA: http://www.businessweek.com/articles/2013-04-12/hacking-an-airplane-with-only-an-android-phone

@reirab, thank you, that's interesting. I'll add that to the answer above. That response itself is quite interesting, for what they don't say - they don't say that the hack can't interfere with the navigation systems, for example. Just that it doesn't allow direct control.

They did say that it "doesn't work on certified flight hardware," though. That would presumably include the navigation systems (of which there are several.)

more ... https://nakedsecurity.sophos.com/2013/04/16/airplane-hack-security-faa/
http://www.foxnews.com/tech/2013/04/12/hacking-in-flight-airplane-did-that-year-ago-hacker-says/
http://venturebeat.com/2013/04/13/renderman-plane-hacks/
http://www.aviationtoday.com/av/web-exclusives/FAA-Dismisses-Aircraft-FMS-Hacking-Claim_78985.html

Based on https://nakedsecurity.sophos.com/2013/04/16/airplane-hack-security-faa/ the agencies seem to be saying that although the hack works on simulators it wouldn't work on actual real-world planes.

@AE bit late :) but in a real aircraft the flight systems and the passenger infotainment and wifi systems are physically separated, no connection whatsoever (except the electrical wiring which draws power from the same generators).


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Why is the Tu-95 so efficient despite having propellers that spin faster than the speed of sound?
I've ready many, many times that propellers are not efficient near the speed of sound because it's so hard to get a tip-speed above Mach 1.
Then I came across this:

It's the Tu-95 "Bear", a propeller-driven bomber whose blade tips actually move faster than the speed of sound. This is the only propeller aircraft I've ever seen whose blade tips do this. There were even reports that submarines' SONARs could hear it from a long way off because those supersonic blade tips were so noisy.
And the plane has a range of 15,000 km. That's pretty good, on par with today's huge commercial airliners.
So how can propellers be very inefficient at supersonic speeds, yet something like this is buildable on propeller-power only?
Edit: Here is the main point of my question: It seems that "all my life" I've been told, "propellers are not efficient at supersonic tip-speeds, and this is what drove the industry to jet power." And yet here is this apparent counterexample, the Tu-95. So how is this possible? What am I missing?
Here is a somewhat related question asking if helicopter blades regularly go supersonic. This is another point I've heard many times: heli blades don't do that because that would make them very inefficient. I'm assuming the rotors are effectively governed by the same laws of efficiency as a propeller for a fixed wing aircraft.
Edit: the B-52 was mentioned in comparison so here are some figures:
$$\begin{array}{|l|r|r|r|} \hline
 \text{Model} & \text{Fuel capacity [L]} & \text{Loaded weight [kg]} & \text{Range [km]}\\ \hline
\text{B-52} & 181,610  & 120,000  & 16,230 \\ \hline
\text{Tu-95} & 95,000  & 171,000  & 15,000 \\ \hline
\end{array}$$
This to me says the Tu-95 is very much more efficient, because it has significantly more weight and significantly less fuel capacity, yet has about the same range.

FWIW, it was the US SOSUS system, https://en.wikipedia.org/wiki/SOSUS, that could detect the "Bears", not necessarily individual submarines...

Long range doesn't necessarily mean it's efficient. It's designed to be a long-range (inter-continental) bomber, so it makes sense that it would have a long range. The U.S. B-52 from the same time period has a slightly higher range at 8,760 nmi (16,230 km,) despite flying significantly faster. That doesn't mean either aircraft was necessarily fuel efficient.

@reirab I edited the OP with that example. If anything, this makes the Tu-95 much more efficient.

@ROIMaison thanks for showing how to put the data in a table, but please be more careful in the future as the figures for B-52 and Tu-95 were mixed up. I swapped them back.

My mention of the B-52 was only to point out that range doesn't imply efficiency, not to say that the B-52 was more efficient.

The XF-84H Thunderscreech also had a supersonic propeller.

@Compro01 Okay that makes 2 that I know of and 1 that's been put into production.

The piston engine tag is erroneous as I believe the Tu-95 uses turboprop engines..

The Bear is extremely loud.  I understood that the noise was due to the contra-rotating propellers.  Each blade on a propeller creates a small shock wave.  When you have contra-rotating propellers, the shock waves from the trailing prop intersect the shock waves of the leading prop.  Where you have 4 blades on each prop, 4 such intersections occur, simultaneously, 4x / revolution.  That adds up to extreme noise levels.  Different numbers of blades between the two props would result in lower amplitude (no simultaneous intersections) and higher frequency (possibly above human hearing range).

@Meower68 not just because they are contra rotating, but the tips produce supersonic vortices which are themselves rather loud already.

Those comparison figures look very odd. I think the 'loaded weight' column tries to compare 2 different items: for the B-52, 120t is the weight with payload but no fuel, for the Tu-95 it seems to be the other way round (fuel but no payload). The B-52 figures also don't add up: it could only carry 181 kl of fuel if it carried no bombs. 181 kl of fuel weighs 140t,  with a loaded weight of 120t and a full fuel load you'd end up way above the stated MTOW.

Yes, propellers have problems at high speed, but if done right, they still have an advantage over turbofans at speeds up to Mach 0.8. Look at the inner engine gondolas of the Tu-95: They are elongated and thicker aft of the trailing edge. This was done to stow the landing gear in them, but also to area-rule the aircraft. The Tu-95 applies knowledge that was gained only in the early jet age. This, of course, also explains the swept wing.
Next, it uses contra-rotating propellers which spin very slowly (just 750 RPM). By having two coaxial propellers spinning in opposite direction, the efficiency at high speed is improved. The first propeller pre-swirls the flow so the flow conditions on the second propeller are more favorable for thrust creation.
The tips of the fan blades of a modern turbofan also move at supersonic speed, so the supersonic propellers on the Tu-95 do not create a direct disadvantage. By keeping the relative thickness of the blade near the tip low, the drag increase can be kept at tolerable levels. But make no mistake: Supersonic flow adds wave drag, and especially around Mach 1 the zero-lift drag coefficient of everything which moves through air has a maximum. It would make the Tu-95 even more efficient if it would fly at a lower cruise speed where the propeller tips are still subsonic, but Tupolev wanted to push the design to the highest useable cruise Mach number.
What you learned about propellers and jets is not wrong, but it is not a black and white world, either. Airliners use jet engines to fly at the highest cruise speed possible, but at the cost of higher fuel consumption. If they would restrict themselves to lower speeds, plenty of fuel could be saved. But too few people would book these flights, because on intercontinental routes they will take noticeably longer. Note that turboprops are still used in regional air traffic, and even the regional jets have lower flight speeds than the intercontinental jets.
Now to the efficiencies of engine types:

Piston engines are the most fuel efficient aviation engines. Their drawback is a constant power output over speed, so that thrust is inverse to speed. This helps for acceleration at take-off, but limits maximum speed. A modern piston engine uses 240 g of fuel for providing 1 kW of power over one hour: 240 g/kW-h. Diesel engines use as little as 220 g/kW-h. This number is already true for the old Jumo 205, among the first aviation diesel engines in operation 80 years ago.
Turboprop engines are next, and their power increases a little over speed due to ram pressure (which will raise the internal pressure in the engine by approx. 30% at Mach 0.8). Their power-specific consumption is about 300 g/kW-h but goes down with increasing size, so the biggest turboprops approach piston engine levels of efficiency.
Jet engines are less efficient than both, but are better for flying fast and high. Their thrust drops even less with speed, so the better basis for expressing consumption is thrust, not power. The typical fuel consumption of a modern jet engine (GE-90) is 30 grams of fuel per Newton of thrust over one hour (30 g/N-h) when run stationary, and twice that in cruise at Mach 0.85. Modern Military jet engines achieve 80 g/N-h at take-off and have roughly constant thrust and specific consumption over speed. Since most innovation happens on turbofans these days, the most modern turbofans again approach piston engine levels of efficiency, but if you compare the same technological standard, they are less efficient than their piston and turboprop contemporaries.

In all cases, thrust is created by accelerating a mass of air backwards. The general equation for propulsive efficiency $\eta$ is $$\eta = \frac{v_{\infty}}{v_{\infty}+\frac{\Delta V}{2}},$$ where $\Delta v$ is the speed increase of the mass of air due to that acceleration. This formula shows that it is better to accelerate a big mass of air only a little than a smaller mass by a lot. Propellers do this and for that reason offer the best efficiency. Turboprops use less efficient, but lighter gas turbines for creating power, but retain the efficient propeller. Civilian turbofans try to increase the mass of air by increasing their bypass ratio, and only the military is using the least efficient types with bypass ratios below 1, because they are the best choice at supersonic speed.
Below you see a plot of the thrust-specific fuel consumption in cruise condition of different engine types over their bypass ratio. The inverse relation is easily visible.

Plot of the thrust specific fuel consumption in lb of fuel per lb of thrust per hour of different engines over the logarithm of their bypass ratio (picture source).
To make a comparison between piston and turbofan engines possible, let's compare fuel consumption at take-off. The formula for static thrust of a propeller is $$T_0 = \sqrt[3]{P^2\cdot\eta_{Prop}^2\cdot\pi\cdot d_P^2\cdot\rho},$$ where $P$ is the shaft power, $d_p$ the propeller diameter and $\rho$ the air density. For our example, we use a four-bladed prop of 3.4 m diameter and an engine with 1111 kW power. Its static thrust is 10.727 kN when we assume standard atmospheric conditions and a prop efficiency of 85%. The fuel flow will be 266.6 kg per hour, and relative to thrust this is 24.8 g/N-h or just 80% of that of a modern turbofan.
I wonder if even the enthusiasts could guess what airplane I used, because I obfuscated it by using those unfamiliar metric units. I guess nobody will argue that it is not optimized for fast flight, so this comparison should also hold for the Tu-95, for which I have less data available.

Here follows the requested expansion on propeller tip speeds. Thanks to the excellent comment by @JanHudec not much is left to say: The propeller diameter is 5.6 m and their speed is 750 RPM, so the circumferential component is $5.6 \cdot \pi \cdot 750 / 60 = 220 m/s$. Add to this the cruise speed of Mach 0.67 (taken from this site — others list quite incredible numbers) at altitude, where the speed of sound is 295 m/s. Mach 0.67 equates there to 197.65 m/s, and vector addition gives 295 m/s for the propeller tips, exactly Mach 1.0. This means that the propeller is subsonic over its whole span.
But the top speed is quite a bit higher. Thanks to the excellent work of Ferdinand Brandner and his team back in the Fifties the NK-12 engines developed already 12,000 horsepower back then, and their power output has since been raised to 14,795 HP. This allows a top speed of Mach 0.82, and now the tip speed comes out at 327 m/s or Mach 1.08 — mildly supersonic. This means that the outer 30% of the propeller experience supersonic flow.
I fail to find a source for the range figures you list in your question. Again I refer to this site: It is 7,800 miles or 12,552 km at a cruise speed of 400 knots or 179 m/s which equals Mach 0.606 at altitude, resulting in Mach 0.96 for the propeller tips. Therefore, it seems the best range is reached with subsonic propeller tips.

Thank you for this data but could you please add more about propeller tip speed? I edited the OP to emphasize that supersonic tip speeds are supposedly very inefficient and that's where my question comes from. Also, please be more careful when editing my data into a table. The Tu-95 and B-52 had mixed up figures; I swapped them back.

@DrZ214: I did not edit your question; I had all hands full with my answer.

oops. where do i find the revision history? or do I have that privilege yet? I'm still new to the site.

@DrZ214 There's a link at the bottom of your question that says "edited x minutes/hours ago." If you click that, it shows you the full revision history.

@reirab ok thanks, I guess it's me who will be more careful in the future.

750RPM/602pi=78.5 radians per second. (334m/s) / (78.5 rad/s) =4.25m propellor radius. That doesn't seem right for the wingspan of 50.10m here. https://en.wikipedia.org/wiki/Tupolev_Tu-95 If 4.25m was right the combined diameter of all propellors would be 4.25*8=34m, or 34/50.10=68% of the wingspan. That doesn't seem to be the case.

@steveverrill, presumably the 334 m/s would be total magnitude of velocity of the propeller tips including the forward component (where did you get the number, I don't see it in the answer nor on the wiki and it is not speed of sound, which is just around 300 m/s at FL350). At maximum speed 255 m/s the orbital component $\sqrt{334^2-255^2}$ is only 217 m/s and 217/78.5 is just 2.76 m.

"Diesel engines use as little as 200 g/kW-h" Pfft. Volkswagen can use way less than that!  Oh, wait...

@JanHudec 1. There are many different values for the speed of sound in the low 300's depending on conditions. The Wikipedia article on the speed of sound gives 343.2m/s. Its possible I transposed the digits by mistake. 2. The question clearly states that the tips "spin" faster than the speed of sound. I felt something didn't add up, got curious and checked it. Either way they are some huge propellors.

@steveverrill, speed of sound is a function of temperature. At average (ISA) temperature at FL350, the speed of sound is 301 m/s. It does not get much lower than that, because temperature only decreases up to tropopause and that is not much higher. But of course the important point is that the tips are supersonic when the forward speed is added.

Piston engines more fuel-efficient than turbine engines?  That can't be right: Reciprocating engines are generally half as efficient as turbine engines.  You must be meaning to say something different, or have omitted some critical qualification.

@feetwet: A piston moving in a cylinder is quite an efficient compressor. Maybe you need to work on your prejudices.

NIce answer. Just a quick comment: I think the precise term is contra rotating props, not counter rotating

@BenSchwehn: Yup, missed that. Added the obligatory Wikipedia link, too. Thanks for your help!

How much of the efficiency advantage is merely down to a slower cruise speed?

@RobinBennett: You are correct, flying more slowly should help regardless of Mach effects. The details depend on the wing loading and cruise altitude, and I would expect that the Tupolev design office optimized the design for Mach 0.7 (the Tu-114 economical speed was Mach 0.71) and added the Mach 0.82 capability only for flight over hostile territory. At the same altitude, a 15% higher speed would reduce L/D by only 8%.

This is not a Tu-95 specific answer. Keep in mind that a propeller produces force in the same manner as an airplane wing. Subsonic and supersonic wings both produce lift, though using very different design profiles. I would get a good, close look at the propeller to see how the tip area is designed. It may be diamond-shaped, like a supersonic airfoil, or it may be very flat, where the function is not lift, but to reduce vortex energy loss, like that of newer commercial aircraft. As long as the supersonic portion of the propeller does not have the profile of a subsonic airfoil, it will not produce the undesirable effects.

It is actually not unusual for tip speeds to go supersonic. In fact, just about every modern turbofan does it at high thrust settings. Next time if you take a plane, sit at a window seat ahead of the engines where you can "see" the fan blades. During take off you will hear an unmistakable buzz from the fan. That is characteristics of supersonic tip speeds. You will also notice that the latest design have a sudden reverse sweep on the blades near the tips. That is for shock mitigation.

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What does the last digit mean in a Piper Arrow model number?
The Piper Arrow's model is PA-28R-201. At first, I thought that 201 means horsepower but the Arrow's HP is 200 so I figured that's not the case. What does it stand for?

The number notes the model
PA-28R-180 180bhp Cherokee Arrow with the ‘Hershey Bar’ wing.
PA-28R-200 200bhp Arrow II with the lengthened fuselage.
PA-28R-201 200bhp Arrow III with the tapered wing.
PA-28RT-201 200bhp Arrow IV with the tapered wing and T tail.
PA-28RT-201T Turbocharged Arrow IV.
The Arrow III was introduced in 1977 with the tapered wing and larger stabilator.  This improved low speed handling characteristics and increased the total fuel capacity from 50 to 77 gallons.

The 200 was the tapered wing and the stretch.  201 is just the GW change.

Not according to the type certificate.  Those were features of the Arrow III, not the II. (http://www.airweb.faa.gov/Regulatory_and_Guidance_Library/rgMakeModel.nsf/0/a44b41c7e7d7d7458625753c004f4a2d/%24FILE/2A13.pdf)

Ok I was going by Wikipedia, and I forgot my normal golden rule to NEVER TRUST FREAKIN' WIKIPEDIA!!! lol

I think the list is incomplete as there are some 200 HP Piper Arrow I models. Only the very first ones were 180 HP but they switched to 200 HP before the Arrow II. This small detail would make impossible to distinguish from Arrow I (200) and II as both would be PA-28R-200

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text:
What is the specific consumption of an A320 at Mach 0.78 and 11,000 metre altitude?
I am currently doing a dissertation on an electric drive system on planes and I need help. I can't find the specific fuel burn rate for an Airbus A320; if anyone could help it would be great. Also a link or solution to calculating specific fuel consumption and known fuel burn would be much appreciated. It is so I could calculate the fuel used from added weight in the Breguet equation, but there is no average fuel consumption for the formula in kg/Ns.

Take a look at these: https://en.wikipedia.org/wiki/Fuel_economy_in_aircraft

This answer by Peter Kämpf is using the Breguet equation for exactly what you are looking for. I think you can use the parameters from there.

Yeah thanks I seen that question hence why I used these parameters but what I really wanted to know is where 0.000018 kg/Ns came from. Couldn't find it anywhere and for my dissertation something like that would either need to be calculated or reference and obviously cant reference an answer to a question. Not a reliable source.

The $0.000018 \frac{kg}{Ns}$ is the Thrust-specific fuel consumption. Mind the units, $\frac{kg}{Ns}$ vs. $\frac{g}{kNs}$ in the wiki table. $0.000018 \frac{kg}{Ns} = 18 \frac{g}{kNs}$. And, by the way, Peter Kämpf is a reliable source ;-)

You may add into the question description your calculation leading to the figure you put in the comments so that answers can focus on what you haven't already figured out by yourself.

@Bianfable: Actually, this answer is even more to the point.

Thank You guys much appreciated :) Wish me luck in my dissertation and I'm not allowed to reference wiki or any forum. Thanks again :)


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Do pilots ever intentionally land a monowheel glider on the main wheel and a wingtip wheel in crosswind conditions?
Do pilots ever intentionally strike a wingtip when landing a mono wheel glider in gusty crosswind conditions?
I understand the Lazair changed from a mono wheel to a standard tail dragger layout for better cross wind ground handling. What about gliders?
Is doing a two-point high-speed ground roll/landing ever done intentionally, with the mono wheel and wing tip wheels (intentional wing strike), instead of slowing down then dropping the wing just before coming to a stop? Say 10 mph crosswind, gusting to 15mph/max crosswind component.

No.
The lever arm of that glider wing is too long and the ground contact force too hard to control. You risk a tailspin which at touchdown speed might very well include a fractured tailboom.
Glider pilots fly their crosswind approach crabbed and try to keep the wings level. After the flare the ideal landing would include a brief kick on the leeward rudder pedal to align the fuselage with the direction of movement just as the wheel touches the ground, but even a slight sideways movement at the point of contact is no problem. Wing tip contact is avoided at all cost and delayed until the glider has slowed down so the ailerons cannot keep the wings level anymore.
The only exception is when there is no safe landing feasible – say on a rocky slope in the mountains. Then the advice is to sideslip the glider into the ground, hoping that the crashing wing will absorb enough energy to let the pilot survive. But that is a single-point landing and quite different to what you have in mind.
But there is one aircraft that can take off from a two-point (actually, counting the tailwheel, it's three, but two of them are the single main wheel and a wingtip) and that is the Akaflieg München Mü-23 motorglider (picture below, source). Starting from a position 90° to the intended take-off direction and with the wingtip pointing into that direction down on the ground, the pilot opens the throttle and lets the aircraft swing around. By the time the aircraft has completed the 90° course change, the wing is level from the centrifugal force and the speed is high enough to keep it there with the ailerons.

Mü-23 pilot briefing to passengers: Now here's the part where we go "Wheee!"

Touching the main wheel and wing tip would not be very nice and risk a ground loop.
Gliders often have a higher crosswind rating that powered aircraft, I have seen tow planes reach their limits before the glider does a number of times.
I have once on a ground roll due to a failed wheel brake put a wing tip on the ground to steer the glider (at a low speed) as the crosswind was causing the glider to weathercock while still rolling.


text:
In an airplane wing, which control surfaces are primary, and which ones are secondary?

I got this device detail of a wing. Those parts are:

1: wingtip fence, one of the wingtip device beside winglet.
2 & 3: aileron.
4: flap track.
5 & 6: slat.
7 & 8: flap.
9 & 10: spoilers.

2 & 3, 5 & 6, 7 & 8, 9 & 10, are part of controls.
In controlling an airplane (if it really has that pairing devices), if we have to use them one after another, which one is said main (primary) and which is secondary?

This question would benefit from improved grammar. Do you mean to ask what are the primary control surfaces and which are secondary.

Yes my fried. Sometimes I confused to chose the right word. Thank you have informed me that.

Generally speaking, if a wingtip fence or a winglet is there, it's fixed and can't be moved, so there is no question of it being used before or after the others, although since it's always there I supposed you could say it's used before any of the others. I say generally because I seem to recall hearing recently of an aircraft that has a movable winglet in some manner, but that may just be my imagination.
Insofar as labeling is concerned, control surfaces that are split—an inboard and an outboard section—are usually called just that, as in the inboard ailerons and the outboard ailerons.
Different makes of aircraft may have different orders of usage in some manner, but since your image pretty much matches that of a Boeing 747-100/200 (except they have no wingtip fence or winglet), let's use them for explanation.
The inboard ailerons, are always in use. The outboard ailerons come into use when the aircraft is in slow flight (relatively speaking), in other words, when slats/flaps are deployed. It's automatic, the pilots don't have to select using the outboard ailerons specifically.
The flap tracks (what you see on the image are the "canoes" covering the actual flaps tracks) move when the flaps are deployed. The flaps will usually operate fine even if a canoe leaves the airplane in flight (happened to me once), and as I remember you're allowed to defer replacing at least one of them, but with a performance penalty.
The movement of the slats is connected to the deployment of the flaps. Any flap selection results in the inboard slats being extended. On the 747, the inboard slats extend when the flap selection handle is moved to flaps 1°. When flaps 2° is selected, the outboard slats extend.
The flaps are deployed as called for by the pilots moving the flap handle to select whatever degree of flaps they want. On the 747 there are detents at flaps up, 1°, 2°, 5°, 10°, 20°, 25°, and 30°.
The spoilers/speed brakes (whatever you want to call them—the argument still rages—are deployed by the pilots using a handle, pulling it aft deploys them, and the inboard spoilers always deploy. Whether the outboard spoilers deploy depends on aircraft speed as determined by the flap setting: no flap deployment, no outboard spoiler deployment.

Thank you sir for the nice explanation.

The primary flight controls on a conventional fixed-wing aircraft are the ailerons, elevator and rudder.
Since your question is restricted to the wing, only the ailerons are commonly placed on it. However, on modern aircraft, some of the other surfaces are wired to move together with the ailerons. For example, the spoilers or flaps, which are then called spoilerons or flaperons.
The elevator and rudder can be combined into a single set of surfaces in a V-tail, but this solution is not widespread due to its higher mechanical complexity and weight.
The rest of the surfaces on your image are either the winglets, high-lift devices or spoilers.
The flaps and slats are generally deployed at the same time, except in edge cases: the first detent on the flap controls might deploy only the flaps, then the second one would activate the slats as well. This depends on the specific aircraft in question.
Furthermore, on an airliner wing like the one pictured, there would be a bias toward deflecting only the inboard surfaces when flying at high airspeeds, to account for the high dynamic pressure in those conditions.

Actually I want to ask completely control device in the wing and the empennage, but I worry one or more will say my question is to broad. But if you want to explain them too, I will very welcome.

How about the device with more than one in a wing? Say like the slat there are 3. From the color, seems that green is one (number 5) and the yellow is seen as one device (number 6). Are they utilized at the same time? Or more specific, like aileron, which is used turn the airplane beside rudder. But aileron them self there are two: number 2 and number 3: Are they used at the same time? Or just one after another? Say like aileron number 2 then number 3?

I refined the answer a bit, dunno if its clearer now.

FWIW on 747-100/200 aircraft the first detent on the flap controls extends the inboard slats but not the flaps.

@AirCraftLover While the rudder can be used to turn the aircraft, that would result in uncoordinated flight. The primarily purpose of the rudder is to counteract the adverse yaw caused by using the ailerons.

The primarily purpose of the rudder is to counteract the adverse yaw caused by using the ailerons, that I have heard previously. The thing I still don't know, what is the TRIM on both horizontal and vertical stabilizer?

That sounds like a separate question :)


text:
What are the requirements to get a private pilot's license in Indonesia?
I am interested to get license to pilot small civil aircraft (up to max. 4 passengers including the pilot him/herself). I read here that there is no age limitation to get the license as long pass the medical check.
What is the required knowledge to get the license? Is anyone here has the shareable pilot training and testing material?
Edit:
I am and Indonesian and stay in Indonesia. The license I want to get is for private slow aircraft such as Cessna which the speed should not more than 300km/h. Passengers are family members or friends, not commercial.

It helps just a tad if we know what country you're asking about.

I have added more info to get clearer intention. Thank you for your comment.

The Indonesian air regulations include CASR 61 Licensing of Pilots & Flight Instructors, which has all the detailed requirements for getting a Student license (subpart C) and then a Private license (subpart D). To get a more 'friendly' overview of what they really mean, I would look for a local flight school that can explain the practical steps.
Interestingly, the Indonesian regulations appear to be very closely based on the US ones.


text:
Are commercial pilots ranked or graded differently based on the size of the aircraft they fly?
I am not sure whether "rank" or "grade" are the most suitable words for this question. If someone know which the most suitable, please edit this question.
I mean, is the rank of a pilot of, say a Boeing 737, different than the rank of a Boeing 747? And the equivalent to my pilot of Airbus A320 and the pilot Airbus A380 are ranked differently? If different, which one is higher?
This question is related to the airplane's passenger capacity, not to the most advance technology installed in one particular airplane.

To the extent that there is any sort of "rank" amongst airline pilots, seniority comes first.  The most senior pilot gets his choice of aircraft, schedules, vacations, and so on; the next most senior pilot gets his choice from everything that's left, and so on until the most junior pilot gets what's left over that nobody senior to him wanted.  So the pilot hired a month before I was is senior to me, and I'm senior to the pilot hired a month after I was.  Not that this translates into "rank" the way that a lower ranking officer in the military salutes a higher ranking officer -- I'm on a first-name basis with anybody I fly with, and I've flown with the most senior pilot in our company, and if not the very most junior pilot, pretty close to it.
At some airlines, larger aircraft pay more to fly than smaller aircraft, so one could contemplate a "ranking" of sorts in that regard.  The pilot who transitions from the 737 to the 767 gains an increase in pay rate in doing that, so you might infer that 737 pilots are lower "rank" than 767 pilots.  Of course, the most senior pilot on the 737 at that carrier has his choice of schedules, while the most junior pilot on the 767 has a schedule that most would see as less desirable.  So I don't think there's too much stock to put into any idea that just because Allen is flying the 767 and Bill is on the 737, Allen is necessarily a higher "rank".  Especially if he's flying to Timbuktu on weekends in that jet, while Bill enjoys his pick of layovers in San Diego in the winter and Boston in the summer.
And, some airlines don't have different pay rates for different equipment.  This makes for less training burden, as pilots aren't switching aircraft to keep moving up the pay ladder as much.
Some guys will find any distinction that they can to make themselves feel special, or superior, or whatever, but for the most part that isn't all that common.  "You're on a bigger airplane than I am, but I'm flying weekdays and you're stuck on weekend reserve."  Or, "You have a better schedule, but my airplane is bigger than yours."  Honestly, who cares?  We're all pilots, we all started at the bottom, we'll all retire at some point between "here" and #1 on the list, and where "you" are on that progression compared with where "I" am right now doesn't really matter all that much.
Of course, the one very real "rank" distinction, on the flight deck at least, is Captain and First Officer.  But between airplanes, not really so much in my experience.

Thank you for your complete explanation. I voted up this. Yes, my point is regarding the salary, not the military-like rank.

Being certified to fly a certain airplane is a type rating.
There is no ranking of airplanes like you mention. If you have a B737 type rating you are not allowed to fly the B747 or the other way around unless you have the type rating for that aircraft.
The list of type ratings that the FAA uses can be found on their website.
Getting a type rating while you already have one for another class can be easier than if you are getting it from scratch. Though that depends on the exact requirements to get each type rating.

It's probably worth mentioning that a pilot certified for a large, complex aircraft is generally paid more than one for a smaller less complex one.

So, can I say that not a mandatory to hold licence to fly B737 before learn how to fly B747, or so on have to hold licence how to fly A320 before learn how to fly A380? Everyone can chose which airplane's license he want to get even for one just study how to be pilot?

@DJClayworth: that what exactly my point. I was just thinking how to say it, but I was worry if many said off topic or not ethic.

@AirCraftLover When we are talking about airliners, training to fly a specific type is usually paid for by the airline. They tend to send their most experienced pilots to learn to fly their largest aircraft.

@DJClayworth, seems that pilot of B747 is ranked higher than pilot of B737, so does pilot A380 is ranked higher than pilot of A320, even it is not a formal ranking. Is my understanding correct?

You are trying to be too exact about something that isn't exact.


text:
What was the lift equation used by the Wright brothers?

NOTICE: The modern lift equation and the lift equation used by the
  Wright brothers in 1900 are slightly different. The lift coefficient
  of the modern equation is referenced to the dynamic pressure of the
  flow, while the lift coefficient of the earlier times was referenced
  to the drag of an equivalent flat plate. So the value of these two
  coefficients would be different even for the same wing and the same
  set of flow conditions.

Above is a quote from a NASA website (emphasis mine). It's new for me that the Wright brothers applied different calculations to their plane. So, what was the equation used by the two brothers?

I don't think they used a lift equation as we think of it today. Most of the aerodynamic research of the very early 20th century was done in the context of ballistics, not wing design.

The Wright brothers' equation is
$$L=kV^2AC_L.$$
where $C_L$ is the ratio of the $L/D$ of a specific wing (AoA, span, chord, camber, thickness all set and fixed) to a perpendicular board into the wind of the same $A$, $k$ is experimentally obtained, and is specific only to the medium (air or water).
In a sense, the Wright's lift equation is seeing lift from a momentum transfer perspective, i.e. the $kV^2$ term corresponds to the momentum flux of the incoming air, and the term $AC_L$ describes how much downward discharge is produced at the price of how much drag.
While the modern lift equation is
$$L=\frac{1}{2}\rho V^2AC_L.$$
This is derived from the Kutta-Joukowski theorem:
$$L=\rho V\Gamma,$$
where $\Gamma=\int_C{\bf v}\,\mathrm{d}{\bf s}$ is a line integral of the second type around a close and simple route around the wing. $\Gamma$ is proportional to $V$. And $C_L$ is defined as
$$C_L=\frac{L}{\frac{1}{2}\rho V^2A}.$$ $C_L$ is not calculated through analytics, but derived through $A,\rho,V$ as obtained in experiments.


text:
If a twin-engine airplane's propellers both rotate in the same direction, do they still produce a left-turning tendency?
If an airplane with two propellers has both propellers with the same rotation direction (say, both the propellers rotate counter-clockwise as seen from nose to the tail), will  be the four left-turning tendencies still be generated?

https://en.wikipedia.org/wiki/Critical_engine

Related Why does the spiraling slipstream from a propeller hit the left side of the fin?

Yes, for the most part.

Definitely P-factor will still exist and provide a yaw torque in the expected direction.  This is why twin-engined aircraft have a "critical engine".
Engine torque will still produce a roll torque in the expected direction.
Gyroscopic precession will still produce a yaw torque in the expected direction when the aircraft pitches.
The yaw torque from the spiralling slipsteam interacting with the vertical fin-- which is normally quite significant in conventional single-engine aircraft-- is the one effect that may be be greatly reduced in a twin-engine airplane of the usual configuration, since the fin is not located in a strong part of the circulation behind either prop.

Do you have a link how a proper way to calculate the tendencies? My intuition also said that there should be also tendencies.

@AircraftLover-- no I don't

I agree with you regarding the spiraling slipstream for aircraft with a single vertical tail. For a twin with a dual vertical tails set behind the engines, the spiraling slipstream would be similar to a s single engine with a single tail.

No it can not work that way.That is the begining of acceleration in airplane then it will begin to move one side.

As quiet flyer has pointed out, p-factor, gyroscopic precession, and torque will all still be present and act on the aircraft as expected. Think of a front-wheel, a rear-wheel, and a four-wheel drive car. All three will lift the nose/front of the car and lower the rear/tail of the car if slam on the gas at a complete stop like in a drag race.

No, because they turn on different axis which does not coincide with the longitudinal axis of the airplane. Having two propellers turning the same way on the same axis, it would enforce the effect.

How does the separation of the axes make the torque disappear? This seems to contradict classical mechanics.

As the engines rotate clockwise seen from a pilot view (or anti-clockwise from the nose to the tail view), when the engine 2 rotate, will it not hil the vertical stabilizer which will make turn-left tendency?

As long as my deduction comes from observation and not from a mechanical engineer degree, both engines outflow will hit the vertical stabilizers one on each side of the longitudinal axis, having not the torque applied to one of the axis won't let the airplane turn, in my humble opinion, one or both the engines running, since the torque they would apply is not on the longitudinal axis of the plane.

Seems that I have missed this discussion. I apologize.

As I said, if both the propeller are rotating counter-clockwise (seen from nose to the tail), then in my opinion, propeller 2 will generate wind spiral, which it will still hit the vertical stabilizer, then make the airplane forced to turn left.

AirCraft Lover, exactly for the reason the propellers are two, whatever directions they're rotating, the flow will hit the directional stabilizer both sides, hopefully with the same speed airflow. This won't push it one way or the other, imho.


text:
Is the MD-11's third engine slightly nose up?
From my visual inspection, the third engine (the engine on the horizontal stabilizer) is slightly "nose up", especially compared to the engines on the wing. That means, the front part of the engine is lifted slightly. Am I correct? If yes, what is the intention?

Closely related

Yes, there is a slight tilt to the engine. Engines are heavy, so placing them on the tail shifts the center of mass towards the tail, which is not good for stability. To counter this, aircraft with rear engines often tilt the engines slightly, so the thrust they produce can offset their own weight, helping with stability. It's extremely slight though, as large angles can produce major pitch oscillations with power changes (something known as pitch coupling).

I believe it has a 4deg incline to align the exhaust with the drag from the fuselage.
It appears more because the inlet is higher than the engine.
http://drawingdatabase.com/mcdonnell-douglas-md-11/

It may be for the same reason down thrust angle is commonly put into tractor engine mounts - to compensate for pitch up tendency of air craft as they accelerate from added thrust leading to increased velocity.
The third engine of the tri-jet is simply pushing the tail up as thrust is applied.  This is something very beneficial in the event of a power-on stall as it assists the elevator in
lowering the nose.
Adding up thrust in the back to compensate for weight imbalance would have to be questioned from an engineering point of view, as failure of this engine would create a dangerous aft CG imbalance.  It is wise not to rely on thrust or trim to correct an out of safe
range CG.  Better to move the wing back a bit, as long as it is still directionally stable.


text:
Why are the engines of the Airbus A400M slightly tilted down?

Picture: Youtube.
Firstly, are the engines really tilted down? I have tried to check another picture over the net, seems they are really tilted down slightly. But need confirmation from you experts, however.
Second, if it is true, what is the reason?

In flight, they are probably horizontal.

Just about all propeller driven airplanes big and small have the engine thrust line canted down a couple degrees from the wing chord line (not necessarily the longitudinal axis - that depends on the wing incidence), roughly equal to the cruising AOA, so that the thrust line is aligned a little closer to the free stream at cruise.  On the A400 it looks like the nacelles are creating a bit of an optical illusion that exaggerates the effect, although the propellers do appear to be canted a bit relative to the fuselage.  Thrust lines may also be offset to mitigate undesired pitching moments caused by thrust.
Single engine airplanes with the engine on the nose also often cant the engine to the side several degrees as well, to compensate for P factor and torque effects, reducing the amount of fin offset required at the tail.  Look straight down on a typical single like a 172, with the prop stopped horizontally, and you can see the prop isn't quite parallel to the wings.  Once you gain awareness of this you start to notice that most single engine planes you see have engines that are cockeyed, as if they were bent.

Canted down several degree from line chord, or several degree from longitudinal axis?

Thank you for the info about mount the propeller sideway to overcome the P-Factor.

Chord.  As I said, "not necessarily the longitudinal axis" which is a different.  AOA is related to chord line, not long axis.

Thank you John for the nice explanation.

It is very obvious in ATR: https://www.airplane-pictures.net/photo/1316613/g-lmrb-loganair-atr-42-all-models/

As Jeffrey points out in his comment to the question:

In flight, they are probably horizontal.

When that plane is at cruise conditions, it will be in a very slightly nose-up pitch attitude. the thrust line from the props will then be in the direction of travel.

That makes sense. But who is Jeffrey?

he's the author of the comment that preceded my answer.


text:
Why are the leading edges of wings not always made as 'sharp' as possible?
Why is an airplane's wing (the leading edge) not made as sharp as possible to break the air, in the same way that a ship's hull is made sharp to easily break the water?
This is unlike Concorde's nose and most jet fighters' noses, which are made very sharp.

A blunter (less sharp) leading edge allows the wing to operate effectively for a wider range of angles of attack (AoA). The angle of attack is the angle between the approaching airflow and the chord line (as illustrated below)

As you can see, the air has to curve around the leading edge on the upper side of the airfoil. This curvature accelerates the flow and thus creates an area of reduced pressure and thus contributes to the lift of the airfoil.
A sharper leading edge will cause a more intense curvature of the flow and therefore reduce the local pressure even further.
A higher angle of attack will also cause a more intense curvature of the flow with the same effects.
Here's the problem: In order to reach pressure equality between the upper and lower side at the trailing edge of the wing, the pressure will have to increase again as you move further towards the trailing edge.
The boundary layer of the flow doesn't like this at all. Strong pressure gradients will cause the boundary layer detach (generally, the boundary layer is already turbulent for commercial aircraft). A detached boundary layer (stall) causes a drastic increase in drag and decrease in lift and is therefore highly undesirable.
To increase the range of angles of attack at wich the boundary layer stays attached and to allow for a more gradual transition between normal flow and stall, the designers favour a quite blunt leading edge for most commercial and general aviation aircraft. This will increase the drag at zero AoA, but won't force the air to follow a high curvature at positive AoAs.
Supersonic aircraft such as the Concorde and fighter aircraft have to deal with a new type of drag called wave drag. Generally wave drag can be reduced by having sharp leading edges.
Most boats also have to fight against some kind of wave drag (although the fluid dynamics are very different) and therefore also have sharp hulls.
This is a broad generalisation and there are a lot more things to consider in reality. If you want I can go into more detail.

There is one formula binding between force (F), pressure (P), and surface area (A). $$P=\frac{F}{A}$$ or $$F=PA$$ Here, F is drag occurred at the leading edge as the airplane hit the air, the pressure P is pressure occurred at the leading edge as the product of the force over the wing surface. A is the frontal surface area. Is this formula has relation to your explanation?

The total resultant force $F$ on the wing can be calculated by integrating the local pressure $p$ over the total wing area $S$ (upper and lower side): $$F = \iint\limits_S p :dA $$ This is like  applying your formula $F=pA$ to very small sections and then adding them all up. You need to do it this way because the pressure is different at every location. Now the component  parallel to the airflow is what we call drag and the orthogonal component is lift. So essentially drag is the sum of the air "pushing" against the frontal area on the leading side and the air "pulling" on the trailing side.

If the plane is flying at an angle of attack, the frontal area of the wing is a lot more than just the leading edge. Look at the image in my answer: Most of the frontal area comes from the underside of the airfoil. Also, the air isn't really pulling on the trailing side of the wing, it is only pushing with less force than the leading side.

In reality friction is also a force acting upon the wing. The real resultant force is the sum of the pressure forces and frictional forces.

Thank you Felix for your nice explanation.

Btw, do you have a recommended classic book that can teach me how do simple classic airplane? I said classic as I don't want to be too complicated. Many times I found reading new book is much much complicated than read old book.

As long as the aircraft flies subsonically, a sharp leading edge doesn't really have much advantage. Far more important for reducing drag is to keep the flow as laminar as possible.
Simplifying the physics a lot, you can imagine that before a round leading edge, an additional “wedge”† of only slightly higher-pressure air is built up, which can divert the flow around the wing almost as efficiently as a sharp edge would. This works only in the subsonic / transsonic region, because the pressure-forwarding travels as a sound wave, i.e. against a subsonic stream the wedge can be built up against the stream direction, but against a supersonic stream this is not possible. That's why supersonic planes have sharp leading edges, but this leads to its own engineering challenges. Sharp edges in general are less structurally robust and they can easily disrupt the laminar flow.
†Actually, this high-pressure region is not wedge-shaped at all, rather it's a smoothly decaying “baffle”. The crucial point is that it makes a pressure gradient that's pointing up for the air approaching above the center line, and down for the air approaching below it. This accelerates the air out of the way of the wing, so not much of it actually hits the surface. You can look at the pressure in some CFD simulations. https://www.google.com/search?q=airfoil+cfd+pressure

Because at subsonic speeds, the best way to "break the air" is to start pushing it out of the way in front of the wing.
The wings with the round noses travel below the speed of sound, the wings with the sharp noses go faster than the speed of sound. The speed of sound is actually the speed of a disturbance in the air, and if the wing approaches at a slower rate it can announce its presence and start pushing air out of the way.
If the wing approaches faster than the speed of sound, the air does not know that the wing is approaching until it is actually there, and will split suddenly and sharply with a shock wave. The best wingtip shape here is the one that cuts through air like a knife.
Image source
Notice that in boats, only the bow at the surface has a sharp knife-like edge like supersonic wings have, under water the bow is rounded. Water at the surface behaves like air at supersonic speeds, because there water can be easily shocked into the third dimension, above water level. Deeper down water cannot be easily compressed, and the lowest resistance bow shape is rounded, like a subsonic wing traveling through air that behaves in an incompressible way.

Rounder leading edges help the air follow the wing under high angles of attack, they are cheaper and easier to manufacture, and thicker wings are structurally stronger, reducing the weight used for structural rigidity by a big margin.
Like almost everything in aviation/engineering, it's all about trade-offs. Clearly, the advantages mentioned above are more important than the sleekness of sharp leading edges.

The shape of the wing helps determine the lift it creates, and the reaction of the wing when the plane is pitched up enough to stop producing lift (or stalls).  Everything is a tradeoff. Small enough curve to make sufficient lift and be aerodynamic, but not quick to stall when flying slower for landing.   Sharp noses help with flying faster than the speed of sound. The Concorde and the jet fighter are designed for fast flight, the airliner is not. The more rounded nose also allows for weather radar to be installed. In even larger planes, the nose can be tilted up for cargo loading as well.

There is one formula: $$P=\frac{F}{A}$$ or $$F=PA$$ Is any from your explanation related to this equation? F is the drag due to frontal area of the wing, P is pressure that occured at the frontal area, and A is the frontal area.

Don't know. I'm a pilot, but not an aeronautical engineer.  My particular plane model started like with a fast, thin leading edge, that was later changed to a more rounded edge for better low speed handling - the sharp edge would stall too quick, general aviation pilots were having a hard time transitioning into it after flying the more traditional rounded edge wing planes.  Good article here on it  https://www.avweb.com/news/features/Used-Aircraft-Guide-Cessna-Cardinal-225924-1.html  "The 6400 series airfoil was changed to a more conventional 2400-series" the 2400 being more rounded.

The NACA 65-A015 on the '68 had a region of very low induced drag at certain low AOAs (the drag bucket). The Cardinal couldn't go fast enough to get the AOA low enough to exploit that, so the airplane's performance was no better than a 172.  Plus the crappy stall behavior and the need to pay close attention to speed.  They just grafted the forward part of the 172's NACA 2415 onto the '70 Cardinal's wing (which started as a scaled down Centurion wing on the '68).  I put a Horton kit (LE cuff) on my '68 and it totally tamed the low speed issues with no speed penalty.


text:
Is it legal to do a barrel roll?
Is it legal to barrel roll a plane?
Are you allowed with any pilot license?
Are there any requirements for the plane to be allowed to barrel roll?

Yeah I was just finding and posting that too

@Dave that answers the question thanks,  I would vote to close but I don't have enough priviledges

Well, classic lawyer response here: It depends.
Barrel roll is an aerobatic maneuver which, at a minimum, requires the PIC comply with the legal limitations on aerobatic flight per 91.303 and 91.307.
Like any other risk management procedure on a proposed maneuver or mission, ask yourself: is it safe?  Is it legal?  Is it reasonable?
You are PIC - Directly responsible for and the final authority on the operation of that airplane.
SAFE:
What are the known risks associated with this maneuver and how can we minimize those risks?
What other mitigating factors eg MAC, CFIT, etc. can come into play here and how can we minimize them?  Do we have backup and emergency contingency plans available plus time and altitude in case something goes wrong?
Are we flying an airplane which is approved for these kinds of maneuvers?  Is the aircraft in good working order?  What about IMSAFE to assume PIC role in aerobatic flight?  What is your flight currency in both this make and model of airplane and the aerobatic maneuver?
Do we have an appropriate preflight and weather briefing for the proposed flight?  Do the conditions permit safe execution of the mission during the time window of operations?
LEGAL:
Do any of the proposed maneuvers or missions violate FARs, or other local, state, or federal laws?
REASONABLE:
Is the execution of the mission at the proposed place, time and with the planned personnel and equipment reasonable or prudent?  Is there any aspect here that while conforming within safe and legal limitations of airmanship would make this unnecessarily risky?
If any of these are in doubt, don’t fly.  You can be held legally liable under 91.13 Careless and Reckless Operation otherwise.
A barrel roll is a safe, 1G maneuver WHEN PROPERLY EXECUTED and has been performed many times in all types of airplanes.  The ability to do so depends on the aircraft type, pilot’s skill, and time and place.
Many airshow and test pilots have barrel rolled all types of aircraft - the late Bob Hoover and Tex Johnson quickly come to mind.  Keep in mind though, those guys were crazy skilled aviators with thousands of flight hours plus plenty of close calls where they quite frankly scared the s@*t out of themselves and escaped death by a hair’s breadth.  Plenty of other people weren’t so lucky and dug a smoking crater.

I read section entitled “Legal” is basically it’s not illegal if it’s not against the laws, without actually saying what the laws are, which is what I believe the OP was after.

True.  However it can come under scrutiny with the 91.13 Careless and Reckless Operation clause as well.  There are a lot of gray areas within the FARs where you can be held criminally liable, even if the act in and of itself is legal.

This answer is for the US. A parachute is required of everyone when the aircraft is carrying someone who is not a crew member.  The maneuver must not be prohibited by the aircraft flight manual. (Or must it be specifically permitted?)   (Future edit needed.)  And of course you must not exceed the permitted airspeed and G-load parameters.
There is no relation to the license (certificate) the pilot holds.
Actually, this related answer indicates that the airplane or glider must be in the "acrobatic" category: What are the US definition and restrictions on aerobatic flight?. But it's not clear what specific FAR is involved, if any.


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Is it currently possible to build a jet engine with 1,050 kN of thrust? (236,049 lbf)
Do we currently have the engineering know-how to build a 1,050 kN jet engine?
This question originated from the idea of changing a 4-engine aircraft into 2-engines. I chose the A380 since it seems to have the highest takeoff weight.
One A380 engine produces a max of 350 kN. If one engine goes out, the A380 still has 1050 kN available, and per regulations that should be enough even for takeoff. So if we switch to a two-engine aircraft, per regulation we need enough thrust for takeoff even if one engine dies, which means each engine would need 1,050 kN max.
I read this and this. They're in the same context of reducing a 4-engine plane to 2-engines, but do not answer the question if 1050 kN is achievable for a single engine.

Possible duplicate of Why does the 747 have 4 engines instead of 2?

Also related: Can the 747 be re-engined as a twin?

@fooot changed the question to be more direct. Read both of your links but they don't answer if a powerful-enough engine can be built to single-handedly carry the A380.

I may be mistaken, but I recall @terry saying once that you are required to have 2 engines operating at any one time on a 4 engine aircraft (the 747 in his case.)  They weren't even required to change course if one engine went out.  So I wonder if the a380 only needs 700kN to climb?

The current record holder for most powerful jet engine is the GE 90-115b generating 127,000 lbf (594kn) of thrust. For some perspective, it has more thrust than the Titanic and the Mercury rocket that brought Alan Shepard into space combined. You are talking about a single engine twice that size...

@RonBeyer You are talking about a single engine twice that size... meaning what exactly? Just because it doesnt exist doesnt mean its not currently possible. It means, first and foremost, that no one has ever ordered one. Could be because can't build it, or could be because they haven't yet gotten around to designing a giant 2-engine plane.

@JayCarr idk. if 700 kN were sufficient, it would have to be symmetric. If you happen to lose 2 engines on the same wing, i doubt enough rudder authority is available to correct yaw at max thrust.

Do we currently have the engineering know-how to build a 1,050 kN jet engine? would a simple "yes" satisfy you? or a equally simple "no"? or what kind of data do you want?

@DrZ214 If you are worried about to rudder authority to cope with 700 kN of asymmetric thrust, why do you think 1 050 kN would be no problem?

I think this is not a duplicate. The OP ask for the maximum possible thrust for an engine designed with today's technology. The threshold of 1,050kN is here to illustrate the possible application but may not be relevant.

@DrZ214 I wasn't suggesting it wasn't technically possible, I was just giving perspective.

@DrZ214 Maybe, maybe not.  All two engine planes are designed to have enough rudder authority so that if one engine goes out, they can continue to climb.  I don't see why the 747 would have been an exception (and it had a huge tail...)

@Federico A simple yes or no would satisfy me if it came from an actual jet engine engineer. Of course, more data is never bad. In particular, it'd be good to know if the geometries and fuel flow can scale up to the right thrust without scaling up a heat flux into something that can't handle it. I'm sure there are more considerations because I'm not a jet engineer.

@DeltaLima Great point. I was considering something like this: 700 kN thrust coming from 1 engine that's near the fuselage. 350 kN and 350 kN coming from 2 engines on one wing. so one of them is rather far from the fuselage. Pretty sure that far 350 kN creates more torque than a nearby 700 kN. I guess we hafta check it against 1050 and 350 + 350 tho.

@JayCarr Right, exactly. Enough rudder authority so that if one engine goes out, they can continue to climb. 4-engine planes are the same, any single engine can die. But in your first comment you were talking about any 2 engines dying, so I pointed out the severe yawing torque that would entail if they were on the same wing.

@DrZ214 Right, and I pointed out that two engine planes are required to be able to climb with one engine out, meaning they have severely asymmetrical thrust, just as a 747 would have if two engines went out on the same side.  I'm pretty sure that the 747, just like any other airliner, is designed to deal with all the power being out on one side.

Yes -- if by 'jet engine' you include rocket engines.

The limit to the size of turbomachinery is considerably larger than the size of current aero engines.
To estimate how large cores can get, we can look at power plant SCGT. You can get heavy frame turbines as large as 576 MWe for the SGT5 (this is half of a typical nuclear reactor at 1000 MWe). The aeroderivative LM6000 delivers 40 MWe out of a 270 kN turbofan core, and the largest aeroderivative, Industrial Trent 60, provides 60-70 MWe out of a 415 kN thrust turbofan core.
This would suggest an thrust equivalent of 3.5-4 MN or 800,000-900,000 lbf for the SGT5. You can't just fly a frame turbine like this, except in the hold: it's slow to spin up, its speed is on the low side, and it's not certified to aviation standards. But that's just a matter of design. It simply shows the amount of power that can be crammed into a single turbine core.
So, could we make a 1 MN engine? Yes, we are making cores with several times the power. Could we make an airworthy 1 MN engine? With effort, perhaps, of course it would cost money to develop. Would it be as good as the engines we have? That's the million dollar question. Or it would be, and more of a billion dollar one, if there were a market for it.

Is it currently possible to build an engine with 1050kN? No, because there's no design for it, because nobody has asked for it. Jet engine design is not a matter of scaling up existing designs, you can't just drag the corner and make it bigger. You have to model the forces involved to understand what your materials requirements might be, blades, etc. I would expect an engine that powerful would pose some serious engineering challenges which would need to be resolved.
Jet engines have been getting progressively bigger over time, so I have no doubt that if there was a need it could be done provided there's enough investment.
Of course it would require an airplane to be designed to use it - an engine that powerful is going to be very big, you'd need more ground clearance below the wing, or a different engine placement to situate those engines, plus stronger wing structures to handle the forces.

related for the size problem.

Getting conflicting answers, so hopefully it will be decided by citations.

As far as I'm aware there's no technical reason why not, but designing an engine with double the thrust of the current most powerful (GE90-115) would take a vast amount of money and time, especially as nothing on a similar scale has been done so it could not be a derivative design like many engines are, the unit cost would also be huge and it (assuming a high-bypass design) would be enormous so hard to fit onto a plane anywhere. All these combined give the real reason such a thing doesn't exist: given the compromises required, no-one wants one.

To quantify "vast amount of money and time", development of new average size jet engine can cost on the order of 1 billion dollars.  Development of something this size would likely be a 10 billion dollar project, if not more.

Technically yes. Economically no.
While the Meganewton engine is feasible, the number you could sell is so low that nobody will put money into its development. Unless some military feels it needs this engine no matter what, it will not be done.

"the Meganewton engine is feasible": Details Peter?

Glue three GE90's together

Use afterburners!

Getting conflicting answers, so hopefully it will be decided by citations.

Meganewton sounds nice

"Economically no". If Europe built the A380 to carry 500+ people (800+ if you pack them in there), just imagine what China might ask for in the next few decades. If the meganewton engine is feasible, please explain why and maybe add what/where the limit is when scaling up.

Currently, no. The most powerful turbofan engines in production today produce in excess of 120,000lb, but to go from this to 236,000lb in one step would be too much of an engineering challenge and too big a commercial risk.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


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Have there ever been forward-swept horizontal stabilizers, and what would be its advantages?
After going over one of my older questions about forward swept wings, I realize I have never seen a forwards-swept horizontal stabilizer. Do they exist? What would be their advantages, if any?

I think one of the main drawing points for forward swept wings would be the stall characteristics. Because of the way the air flows over the wings, the tips always stall before the root (or so I think I remember). They will also have better controllability in transonic and supersonic speed profiles. I suppose the elevator could have the same resilience to pressure waves from going supersonic, but I don't think the stall characteristics would matter as much.

This is a very interesting question. I too cannot find any aircraft designs with forward-swept horizontal stabilizers.

Forward sweep is chosen when the designers value resistance against tip stall and a rear location of the wing spar higher than low mass. None of those advantages of a forward swept wing has any weight in the design of a horizontal tail, so a forward swept tail has never been selected.

The HFB Hansa , a business jet made in Germany in the 60s used forward swept wings, as did several research jets in the 60s -70s but I don't think any had a forward swept stabilizer.  Forward swept lifting surfaces have the advantages of rearward swept surfaces, delaying shock wave formation to higher Mach number by reducing the effective thickness of the airfoil, without some of the disadvantages, tip first stall, decreased roll response, decreasing effectiveness at high angles of attack.  But the forward swept lifting surfaces have disadvantages as well like, the requirements for much stiffer structure to avoid flutter and more tendency for Dutch roll.
With the advent of fly by wire, and the relaxed stability requirements that go along with it,  the horizontal stabilizer on many new aircraft are operating at very low lift coefficients in cruise so I am not sure if there would be much advantage, except perhaps in a fighter optimized for gun fighting (close in high turn rate, heavily g loaded condition).  The flutter issue is much easier to design for today, since we have extremely high modulus, low mass, graphite fibers we can use but nobody even seems interested in going with a forward swept wing, much less a stabilizer.
The aviation industry seems to have settled into a very conservative mind set after the heady days of the cold war, probably due to the immense cost of developing truly new technologies.  I don't think we are likely to see a production forward swept, wing or tail, aircraft for quite some time.

this is more comment/speculation on your side, rather than an actual answer.

Do you have a better answer, Federico, or just another opinion?
@strato man, there's an example of fwd swept tail that has been in production for a very long time, the Mooney. :)

@JuanJimenez I have neither an answer nor an opinion, but this does not make this post any better.

@federico Your comment is an opinion. I for one disagree with you.

@JuanJimenez good, disagreement is healthy. but you can agree that mine is a comment and not an answer, right?

@federico Yes, it's an opinion. I'm glad we agree. Move on...

@JuanJimenez I moved on a month ago.

@Federico Yes. It shows. Since you are hell-bent on it, I'll give you the privilege of having the last word.


text:
How to build a 2 mile long runway on a 1 mile square island?
On Puzzling.SE I found this question:

You have a 1 mile long x 1 mile wide private island that you wish to
  turn into a resort. A plane requires a 2-miles long runway to take
  off. What do you do?

There are plenty of answers, among them some irrational ones, but also some good approaches to solving this puzzle.
From an aeronautical point of view, what would be a reasonable solution?
I am thinking about a vertically curved runway. To meet the 2 mile requirement it would need to have an angle of (estimated) 25° at the edges of the curved runway. It would go diagonally across the island and by its curvature add the extra length needed to the √ 2 length of the diagonal length.
I am sure there must be a better solution though (extensions of the island shouldn't count!)

The answers to that question already seem to cover most possibilities. Curved runways are discussed here. Sloped runways are discussed here. Both have many issues. Most likely the runway would be extended from the island. You can put an entire airport with runways >2 miles long on an entirely man-made island.

provide helicopters.

@erich Some of the comments on Puzzling also mention that there's a perfectly serviceable 2-mile runway adjacent to the island, provided you have a seaplane.

I repeat my comment from Puzzling SE: an island of that size simply doesn't need a 2-mile runway. The smaller Boeing 737s can take off in less than a mile and an island that's only a mile square doesn't have the capacity for planes of even that size.

@David_Richerby yes that is correct but that is not what this question is about. In Puzzling. SE it is simply about coming up with a solution for the problem (put a 2 mile runway on that island) and here we are looking at this problem from the aeronautical POV.

@Maverick283 Sure. And that is the aeronautical point of view: a 2-mile runway is ridiculously over-specced for the kinds of plane that would need to visit that island. If answers along the lines of "Don't bother: use seaplanes instead" are acceptable, then so is "Don't bother: build a runway long enough for the kinds of plane that might be needed for a location of that size."

Maybe the space shuttle wants to check it out eventually ;)

I've spent some time clarifying the problem in the source puzzle. @PeterKämpf's answer below is one solution - as an alternative, I'd be interesting to know whether banked curves on a runway allow takeoff to be physically feasible.

@AE One problem with banked curves is that being in a turn increases the load factor, such that lifting off in a turn requires a greater airspeed than lifting off from a straight takeoff roll. As far as I can immediately see (very back of the envelope), this would tend to cancel out the extra length you can get from a curved runway of constant radius. A banked turn just before the point where the plane reaches $v_1$ followed by a straight section to actually lift off from might have a better chance of working (on paper!).

To those that have voted to close this question as off-topic, why? It seems perfectly on-topic to me.

Good tutorial for the construction: Kansai International Airport

Anyone who has ever flown at Zar (EPZR) in Poland knows how much a runway slope can reduce the needed field length. For aircraft which need a 2 miles long level runway, a 1 mile long one with a 15% slope at its end will do just fine. Make the slope shallow at the bottom and increase it the further up the runway goes, just like the hillside runway at Zar. If the end point is 183.5 m higher than the touch-down point, the height difference is equivalent to a speed reduction from 60 m/s to zero.
Take-offs work in the opposite way, giving the same speed boost on the way down. A 1 mile long runway will do just fine. You do not even need to run it diagonally across the island.
Yes, this does not exactly answer the riddle, but is an engineering solution to a simple problem.

This actually appears to be correct answer to the original question as well. The question specifically mentions 2 miles of flat runway and being on Earth, which leads me to think that the effect of slope on acceleration/deceleration should be included.

A 15% slope would put your mile long runway at 15% of a mile up, 792 feet. Assume 200 feet wide, this would require 5280792200/2 = 418 million cubic feet of earth. Given this island is only 5280x5280 feet already, (28 million square feet) this would lower the average height of the island by 15 feet. I wouldn't be surprised if this island wasn't even that high at its maximum point! There literally may not be enough earth to do this locally, unless perhaps you can find boulders in the sea to act as filler.

@corsiKa: By no means I intended to say that the runway slope is 15% over its total length! It starts horizontally (That is the meaning of "shallow at the bottom"), so aircraft have a level touchdown zone. Only at the rollout end will it have more slope. Like the runway in Zar.

@corsiKa - there is no requirement that all material for the runway be sourced locally (I doubt said island has the material for making the concrete/tarmac for the runway surface), so there's no issue with shipping in all the fill dirt or dredging it from the water surrounding the island. Dredging that much dirt would have the added bonus of lowering the ocean's surface enough to expose more island for you to play on! (that's a joke...)

As an aside (but a potentially relevant one), it is a certificate limit for many commercial airliners that the runways they operate on must have only up to 2% slope (up or down). More than that would be prohibited for these aircraft.

@CptReynolds: The FAA considers 2% to be the limit for commercial airports, but there is no law forbidding manufacturers to qualify their planes for steeper runways. The Dash-7s operating out of Courchevel flew regularly from a strip with 18% slope.

That's true of course. I was coming at it from a commercial jet airliner view, and the types I have worked with (mainly Boeings) were all certified to +/- 2% slope. As you say, Boeing would have been at liberty to choose a higher value if they had so wished.

Instead of a constant-slope inclined runway, why not use a Brachistochrone curve ramp?  You get the added benefit of a ski jump at the end. :-D Oh, wait--landings might be a little tricky. Oh, well...

A seaplane would be a suitable solution.  Then the only infrastructure required on the island is a jetty and fuel/servicing.
This also enables a much larger aircraft and so easier cargo resupply and a longer range on the aircraft.

It certainly enables much larger aircraft, but most sea planes these days are on the smaller side. Still a very viable option.

@foot There are a number of large seaplanes still being manufactured.  The dominant use is as fire bombers and as air sea rescue but they are being made.  There is even an unmanned cargo seaplane in development link

Joni, at best the flying boats currently in production (Beriev, Bombarier) are medium, not large. Large is something like the Martin Mars or BV 222.

@egid  How large does large have to be and how big is medium?  They certainly aren't building any on the scale of the Hercules HK-1 but large seaplanes are still being built.  The Question did not specify any cargo requirement.  My original point was merely that the use of a seaplane enabled a larger aircraft that was not limited by the sqrt(2) mile long runway possible on the island.

I would say that aircraft sizes for landplanes and seaplanes should be interchangeable. By that definition the CL-415 is not large!

There really isn't a better answer than "extending the island." To function, runways must be straight (or very nearly so, a half-mile radius of curvature is unacceptable at takeoff speeds), and level (or very nearly so, gradients are measured in percent and 11% is an extreme gradient, which still gets you very little extra length). However, aircraft carriers in a lot of countries have ski-jump ramps which seem to go up to 12 degrees (20% gradient or so, let's be generous and say 15 degrees), which means that's probably a good absolute limit on the slope of the runway anywhere (it doesn't work on the whole runway, but this is irrelevant). Let's look at some numbers. We'll start with the longest possible flat runway, and then put it at the highest possible slope, to get an upper bound on length.
The largest radius of curvature you can have horizontally is 1 mile; this is also a very high radius of curvature (around what the Endless Runway people have; a comment on the curved runways question calculates that at takeoff speed, you need the equivalent of a 20-degree bank to stay on this runway), so anything tighter won't be acceptable. This gives you $2\pi/4\approx1.57$ miles; this is the longest possible flat runway.
You might also curve up while doing this; the maximum slope at any point is 15 degrees. The longest way to do this is to have a constant 15-degree slope; this means that the max possible length, with tight horizontal curvature and a ridiculous slope, is $1.57/\cos 15^\circ\approx1.63$ miles.
So there you have it. The maximum length available, with extremely generous slope and curvature constraints, is well under 2 miles.

I will go through some answers of the puzzle, some rational, some not:
Add a third dimension (i.e. sloped diagonal runway):
Your plane will be going downslope at a 45 degree angle. It will pick up speed pretty fast, but requires a skillful pilot to pull it out of the dive before hitting water. Not very practical.
If you go upslope, your pitch up will be 45 degrees and you will likely have insufficient engine power to maintain airspeed (not to mention accelerate). Not feasible either.
Do we really need 2 miles?
If the plane needs 2 miles due to the low acceleration of the engine, then we can use a bit of slope (e.g. 5 or 10 degrees) instead of 45. A fully vertical acceleration gives 9.8 ms-2. A 10 degrees slope will give the plane an additional acceleration of $9.8 sin(10^\circ)$ ms-2 on top of the acceleration given by the engine. This has the hope of significantly shortening the takeoff distance if the engine is weak.
Aircraft Catapult
This one has been done practically, given a strong enough catapult and reinforced aircraft frame.
My personal answer...

 Wait for enough head wind to takeoff!

Wait for typhoon. 2) Make sure the runway is open.

Curved runways have many issues. Especially in bad weather, aircraft sometimes run off of straight runways, so a curved one would be even harder to stay on. The curve would also increase the distance needed for both takeoff and landing, meaning that even more than 2 miles would be needed.
Sloped runways do exist. However, sloped runways like EPZR (mentioned by Peter Kämpf) or Lukla tend to be small (both are less than 2000 feet, EPZR is not paved). The physics limit the runway to operating in one direction only. Though wind becomes less of a factor, the issues still prevent this from being used for large airports.
Another issue is the height of the high end of the runway. Zar and Lukla are both located in terrain that requires one end of the runway to be raised. A 1-mile square island would probably not be shaped this way. Even if it is, if an airplane goes off the runway, or needs to abort a takeoff or landing, the slope will make this much harder. The pilots would also have to adjust their takeoff and landing technique to account for the slope, which will probably result in many more hard landings and tail strikes. A sloped runway may be acceptable for small aircraft and short runways, but typical aircraft needing 2 miles of runway will be much more difficult to operate this way.
Some aircraft carriers solve the runway length issue with a slope only one the very end. However, this is most helpful to aircraft like the Harrier that already can provide some vertical thrust, and the aircraft must still perform an arrested landing. Other carriers use a steam catapult to assist takeoff, which requires much more maintenance but is capable of launching heavier aircraft.
Using a sea plane to land on the water is another option. However, aircraft on the scale of needing a 2 mile runway are typically not sea planes. If you are going to design a new plane, you might as well design one that can operate to the runway length requirement.
Another fun option is jet-assisted takeoff (JATO). Rocket engines are strapped to the plane to accelerate it to takeoff speed more quickly. These can be used for landing as well, but that is a bit more difficult.
Do to the issues with these options, large airports in need of land tend to just make more land. You can put an entire airport with runways >2 miles long on a completely man-made island. There is typically enough room around an island that creating an extension is not an issue.

The answer is to extend the island, the main issue I see here is that you really cant change any of the other variables.
A catapult wont work because (as far as I know) modern airlines do not have the airframe necessary to support this. Then again I may be wrong but I would think they could not take that kind of force.
I have no idea how a ski jump like slope would affect an aircraft. I know they have them on aircraft carriers so maybe someone could weigh in on how that works both for plane size and the effect it has on the airframe from a force on the gear perspective.
Sea planes would still require people to come into a local airpot and take a smaller seaplane to the island assuming it was near a larger airport. Or take a sea plane of a certain vintage, capable of flying long distances.
Extending the runway (depending on the surrounding sea bed) is not very difficult and has been done. KIX in hong kong is build on a completely man made island so adding some land to the end of the island it not a big deal. I also add this since I assume you want the ability to fly direct to the island and not have to fly to a larger airport then take a small plane into the island.

Maybe unconventional, but it has been done: Make a ramp out over the water that is a runway extension.
Funchal (Madeira) is an example where that was done (though not nearly as long as your requirements).
http://www.getalookatthis.com/2008/01/17/new-airport-runway-in-portugal-part-3/ has photos of the runway extension under construction.
Another solution, if you're at low altitude and the water is shallow, may be to not build on pillars but landfill/reclaimed land.
This is being suggested for New York La Guardia, and of course Osaka Kansai airport takes this to the extreme by being built on an artificial island, offshore from the city because there was no space there.